I just stumbled on this paper from earlier this year by Joakim Ruist. Here’s the abstract:

This paper aims to explain the high intergenerational persistence of inequality between groups of different ancestries in the US. Initial inequality between immigrant groups is interpreted as largely due to differently strong self-selection on unobservable skill endowments. These endowments are in turn assumed to be more persistent than observable outcomes across generations. If skill endowments are responsible for a larger share of total inequality between immigrant groups than between individuals generally, the former inequality will be more persistent. This explanation implies the additional testable hypothesis that the correlation between home country characteristics that influence the self-selection pattern – in particular the distance to the US – and migrants’ or their descendants’ outcomes will increase with every new generation of descendants. This prediction receives strong empirical support: The migration distance of those who moved to the US around the turn of the 20th century has risen from explaining only 14% of inequality between ancestry groups in the immigrant generation itself, to a full 49% in the generation of their great-grandchildren today.

Here’s a paragraph from the conclusion:

The policy relevance of this result lies to a large extent in what it does not say. It is well known that inequality between ancestry groups in America is highly persistent, and also that some groups experience more mobility than others. Previous explanations for this to some extent indicate that something is “wrong”, in that certain groups’ upward mobility is hampered either by these groups’ own behavior, or American society’s behavior towards them. As such they also indicate a role for policy in improving the situation. In contrast, according to the results and interpretation reported here, ancestry groups’ low socioeconomic mobility is not an indication that something is wrong, but merely that the impact of migrants’ self-selection is longer-lasting than previously thought.

Here’s the last paragraph in the paper:

Finally these results say something important not only about migrants’ self-selection and intergenerational mobility, but also about America. In the 19th century, many millions of Europeans dreamed of a new life in America. But the journey was costly, and at least until the arrival of transatlantic steamships even dangerous, and only some actually made the leap. The results reported in this study not only support the view that those who actually did make the journey were equipped with qualities not equally possessed by all of those who did not. They also tell us that these qualities remained for several generations with their descendants, who made their native country the global hub of knowledge, innovation, entrepreneurship, and industry of the 20th century.

The modern era being what it is, I imagine that today, in some countries, it is easier to be a migrant than to stay put. Ruist’s paper would imply that immigrants from such countries might, on average, have multiple generations of descendants with particularly low SES scores.